Richtmyer-Meshkov instability: theory of linear and nonlinear evolution

Laser astrophysics experiment on the amplification of magnetic fields by shock-induced interfacial instabilities

Laser experiments are becoming established as tools for astronomical research that complement observations and theoretical modeling. Localized strong magnetic fields have been observed at a shock front of supernova explosions. Experimental confirmation and identification of the physical mechanism for this observation are of great importance in understanding the evolution of the interstellar medium. However, it has been challenging to treat the interaction between hydrodynamic instabilities and an ambient magnetic field in the laboratory. Here, we developed an experimental platform to examine magnetized Richtmyer-Meshkov instability (RMI). The measured growth velocity was consistent with the linear theory, and the magnetic-field amplification was correlated with RMI growth. Our experiment validated the turbulent amplification of magnetic fields associated with the shock-induced interfacial instability in astrophysical conditions. Experimental elucidation of fundamental processes in magnetized plasmas is generally essential in various situations such as fusion plasmas and planetary sciences.

Suppression of the Richtmyer-Meshkov instability due to a density transition layer at the interface

We have investigated the effects of a smooth transition layer at the contact discontinuity on the growth of the Richtmyer-Meshkov instability (RMI) by hydrodynamic numerical simulations, and we derived an empirical condition for the suppression of the instability. The transition layer has little influence on the RMI when the thickness L is narrower than the wavelength of an interface modulation λ. However, if the transition layer becomes broader than λ, the perturbed velocity associated with the RMI is reduced considerably. The suppression condition is interpreted as the cases in which the shock transit time through the transition layer is longer than the sound crossing time of the modulation wavelength. The fluctuation kinetic energy decreases as L^{-p} with p=2.5, which indicates that the growth velocity of the RMI decreases in proportion to L^{-p/2} by the presence of the transition layer. This feature is found to be quite universal and appeared in a wide range of shock-interface interactions.

Supernova, nuclear synthesis, fluid instabilities, and interfacial mixing

Supernovae and their remnants are a central problem in astrophysics due to their role in the stellar evolution and nuclear synthesis. A supernova's explosion is driven by a blast wave causing the development of Rayleigh-Taylor and Richtmyer-Meshkov instabilities and leading to intensive interfacial mixing of materials of a progenitor star. Rayleigh-Taylor and Richtmyer-Meshkov mixing breaks spherical symmetry of a star and provides conditions for synthesis of heavy mass elements in addition to light mass elements synthesized in the star before its explosion. By focusing on hydrodynamic aspects of the problem, we apply group theory analysis to identify the properties of Rayleigh-Taylor and Richtmyer-Meshkov dynamics with variable acceleration, discover subdiffusive character of the blast wave-induced interfacial mixing, and reveal the mechanism of energy accumulation and transport at small scales in supernovae.

Effects of the Atwood number on the Richtmyer-Meshkov instability in elastic-plastic media

The Richtmyer-Meshkov instability of small perturbed single-mode interfaces between an elastic-plastic solid and an inviscid liquid is investigated by theoretical analysis and numerical simulation in this work. A modified model including the Atwood number effect is proposed to describe the long-term behaviors of small perturbations at the solid-liquid interface. In contrast to an effective theoretical model at the solid-vacuum interface, this model is appropriate at different Atwood numbers. Owing to the effect of elastic-plastic characteristics and the density ratio, the evolution of the spike amplitude exhibits nonlinear mechanical behavior. As the absolute value of the Atwood number decreases, the maximum spike amplitude also decreases. To validate this model, an Eulerian finite-difference multicomponent code is adopted to study the time evolution of the spike amplitude at different Atwood numbers. The model coefficients are obtained by analyzing the relevant characteristic statistics collected from the numerical results. Under different initial conditions such as Atwood number and shock strength, the applicability of this modified model is verified by comparing the numerical results with the model profile. The consistency in results signifies that the modified model is not only suitable for specific shock intensity and Atwood number, but also adaptable within a certain range.

Interface dynamics: Mechanisms of stabilization and destabilization and structure of flow fields

Interfacial mixing and transport are nonequilibrium processes coupling kinetic to macroscopic scales. They occur in fluids, plasmas, and materials over celestial events to atoms. Grasping their fundamentals can advance a broad range of disciplines in science, mathematics, and engineering. This paper focuses on the long-standing classic problem of stability of a phase boundary-a fluid interface that has a mass flow across it. We briefly review the recent advances in theoretical and experimental studies, develop the general theoretical framework directly linking the microscopic interfacial transport to the macroscopic flow fields, discover mechanisms of interface stabilization and destabilization that have not been discussed before for both inertial and accelerated dynamics, and chart perspectives for future research.

Knudsen-number dependence of two-dimensional single-mode Rayleigh-Taylor fluid instabilities

We present a study of single-mode Rayleigh-Taylor instabilities with a modified direct simulation Monte Carlo (MDSMC) code in two dimensions. The MDSMC code is aimed to capture the dynamics of matter for a large range of Knudsen numbers within one approach. Our method combines the traditional Monte Carlo technique to efficiently propagate particles and the point-of-closest-approach method for high spatial resolution. Simulations are performed using different particle mean free paths and we compare the results to linear theory predictions for the growth rate including diffusion and viscosity. We find good agreement between theoretical predictions and simulations and, at late times, observe the development of secondary instabilities, similar to hydrodynamic simulations and experiments. Large mean free paths favor particle diffusion, reduce the occurrence of secondary instabilities, and approach the noninteracting gas limit.

Normal velocity freeze-out of the Richtmyer-Meshkov instability when a rarefaction is reflected

The Richtmyer-Meshkov instability (RMI) develops when a shock front hits a rippled contact surface separating two different fluids. After the incident shock refraction, a transmitted shock is always formed and another shock or a rarefaction is reflected back. The pressure-entropy-vorticity fields generated by the rippled wave fronts are responsible for the generation of hydrodynamic perturbations in both fluids. In linear theory, the contact surface ripple reaches an asymptotic normal velocity which is dependent on the incident shock Mach number, fluids density ratio, and compressibilities. It was speculated in the past about the possibility of getting a zero value for the asymptotic normal velocity, a phenomenon that was called "freeze-out" [G. Fraley, Phys. Fluids 29, 376 (1986); K. Mikaelian, Phys. Fluids 6, 356 (1994), A. L. Velikovich et al., Phys. Plasmas 8, 592 (2001)]. In a previous paper, freeze-out was studied for the case when a shock is reflected at the contact surface [J. G. Wouchuk and K. Nishihara, Phys. Rev. E 70, 026305 (2004)]. In this work the freeze-out of the RMI is studied for the case in which a rarefaction is reflected back. Two different regimes are found: nearly equal preshock densities at the interface at any shock intensity, and very large density difference for strong shocks. The contour curves that relate shock Mach number and preshock density ratio are obtained in both regimes for fluids with equal and different compressibilities. An analysis of the temporal evolution of different cases of freeze-out is shown. It is seen that the freeze-out is the result of the interaction between the unstable interface and the rippled wave fronts. As a general and qualitative criterion to look for freeze-out situations, it is seen that a necessary condition for freeze-out is the same orientation for the tangential velocities generated at each side of the contact surface at t=0+. A comparison with the results of previous works is also shown.

What is certain and what is not so certain in our knowledge of Rayleigh-Taylor mixing?

Past decades significantly advanced our understanding of Rayleigh-Taylor (RT) mixing. We briefly review recent theoretical results and numerical modelling approaches and compare them with state-of-the-art experiments focusing the reader's attention on qualitative properties of RT mixing.

Critical magnetic field strength for suppression of the Richtmyer-Meshkov instability in plasmas

The critical strength of a magnetic field required for the suppression of the Richtmyer-Meshkov instability (RMI) is investigated numerically by using a two-dimensional single-mode analysis. For the cases of magnetohydrodynamic parallel shocks, the RMI can be stabilized as a result of the extraction of vorticity from the interface. A useful formula describing a critical condition for magnetohydrodynamic RMI is introduced and is successfully confirmed by direct numerical simulations. The critical field strength is found to be largely dependent on the Mach number of the incident shock. If the shock is strong enough, even low-β plasmas can be subject to the growth of the RMI.

Renormalization group approach to interfacial motion in incompressible Richtmyer-Meshkov instability

Nonlinear interfacial motion in incompressible Richtmyer-Meshkov instability is theoretically investigated using the renormalization group approach. The amplitude equation describing the asymptotic interfacial motion is derived using this approach. A comparison with calculations carried out by the weakly nonlinear analysis is performed for various Atwood numbers and the validity of the renormalization group approach is discussed. We show that this approach suppresses the divergence in the perturbative solutions obtained by the weakly nonlinear analysis and provides better approximations for the growth rate of bubbles and spikes and interfacial profiles at the asymptotic nonlinear stage without requiring the use of Padé approximants.

Turbulent mixing and beyond

Turbulence is a supermixer. Turbulent mixing has immense consequences for physical phenomena spanning astrophysical to atomistic scales under both high- and low-energy-density conditions. It influences thermonuclear fusion in inertial and magnetic confinement systems; governs dynamics of supernovae, accretion disks and explosions; dominates stellar convection, planetary interiors and mantle-lithosphere tectonics; affects premixed and non-premixed combustion; controls standard turbulent flows (wall-bounded and free-subsonic, supersonic as well as hypersonic); as well as atmospheric and oceanic phenomena (which themselves have important effects on climate). In most of these circumstances, the mixing phenomena are driven by non-equilibrium dynamics. While each article in this collection dwells on a specific problem, the purpose here is to seek a few unified themes amongst diverse phenomena.